Details

Time bar (total: 16.2s)

sample220.0ms

Algorithm
intervals
Results
92.0ms95×body1280valid
60.0ms28×body2560valid
25.0ms51×body640valid
10.0ms94×body80valid
7.0ms25×body320valid
6.0ms1×body5120valid
5.0ms61×body80nan
2.0ms8×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.2b
(pow (+ 1.0 (/ i n)) n)
9.9b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite596.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 281
Calls
4 calls:
243.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
110.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
212.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
379.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
247.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
407.0ms
(pow (+ 1.0 (/ i n)) n)
359.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012263285
150023166

prune804.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
0.1b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.9b
(* (pow i 2) (log 1.0))
18.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
111×add-sqr-sqrt
90×add-cube-cbrt *-un-lft-identity
56×associate-*r*
28×add-exp-log
22×add-cbrt-cube
14×associate-*l*
13×associate-/r*
11×unswap-sqr
9×prod-exp div-inv
8×unpow-prod-down
7×pow1
6×cbrt-undiv log-prod div-exp
5×cbrt-unprod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num log-pow flip--
Counts
4 → 200
Calls
4 calls:
6.0ms
(* 0.5 (pow i 2))
141.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
7.0ms
(* (pow i 2) (log 1.0))
135.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series573.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 0.5 (pow i 2))
215.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
142.0ms
(* (pow i 2) (log 1.0))
191.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify159.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09073549
147873275
250013275

prune780.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
2.3b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
11.9b
(* (pow i 2) (log 1.0))
13.4b
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
136×add-sqr-sqrt
98×*-un-lft-identity
96×add-cube-cbrt
58×add-exp-log
56×associate-*r*
34×add-cbrt-cube
24×associate-*l*
23×div-exp
16×prod-exp unswap-sqr
13×associate-/r*
12×cbrt-undiv
10×div-inv
8×unpow-prod-down cbrt-unprod
7×pow1
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ clear-num log-pow flip--
Counts
4 → 229
Calls
4 calls:
6.0ms
(* 0.5 (pow i 2))
133.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
7.0ms
(* (pow i 2) (log 1.0))
153.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 0.5 (pow i 2))
147.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
143.0ms
(* (pow i 2) (log 1.0))
211.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify69.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011334294
150013845

prune703.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.6b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
5.8b
(* (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) (cbrt (/ 100.0 i)))
7.1b
(* (* (cbrt (/ 100.0 i)) (cbrt (/ 100.0 i))) (* (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) (cbrt (/ 100.0 i))))
11.9b
(* (pow i 2) (log 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
41×associate-*l/
39×cbrt-div
37×add-exp-log
33×pow1
31×frac-times
27×add-sqr-sqrt
24×associate-*r*
22×prod-exp add-cbrt-cube
20×cbrt-unprod
19×add-cube-cbrt *-un-lft-identity pow-prod-down
16×associate-*r/
13×cbrt-prod associate-*l*
11×flip3-- flip--
9×times-frac
6×log-prod
5×unswap-sqr
4×unpow-prod-down *-commutative add-log-exp
3×distribute-rgt-in distribute-lft-in
2×unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow div-inv
Counts
4 → 141
Calls
4 calls:
198.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
248.0ms
(* (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) (cbrt (/ 100.0 i)))
647.0ms
(* (* (cbrt (/ 100.0 i)) (cbrt (/ 100.0 i))) (* (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) (cbrt (/ 100.0 i))))
12.0ms
(* (pow i 2) (log 1.0))

series908.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
326.0ms
(* (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) (cbrt (/ 100.0 i)))
294.0ms
(* (* (cbrt (/ 100.0 i)) (cbrt (/ 100.0 i))) (* (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) (cbrt (/ 100.0 i))))
143.0ms
(* (pow i 2) (log 1.0))

simplify124.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
08873302
141292806
250012735

prune468.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 9.6b

regimes221.0ms

Accuracy

43.9% (12.4b remaining)

Error of 23.8b against oracle of 11.3b and baseline of 33.5b

bsearch696.0ms

Steps
ItersRangePoint
9
9.202643273762206e-197
2.0876742698074505e-190
3.2149863127016826e-193
10
-4.019062342740625e-179
-4.921752557888658e-193
-3.0810685690551663e-191
4
-3.016982961048864
-1.7081313977704333
-1.9832551762171204
8
-4.442583579136125e+124
-2.124845354426568e+121
-4.2000617866809285e+124
9
-3.595183515363578e+216
-5.440966681527398e+209
-5.513680821791014e+209

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07876
17876

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.2s2430×body1280valid
2.1s994×body2560valid
751.0ms1721×body640valid
302.0ms3074×body80valid
243.0ms846×body320valid
159.0ms2273×body80nan
89.0ms462×body160valid
33.0ms9×body5120valid